Page 359 - Advanced Thermodynamics for Engineers, Second Edition

16.2 FURTHER CONSIDERATIONS OF BASIC ENGINE CYCLES 349

For the air-standard cycle the thermal efficiency is only a function of compression ratio, r.
The imep can be evaluated from Eqn (16.8).
With r ¼ 7,
1 1 10 43000 1
5
bar
p ¼ 1 k 1 5
r 0:287 373 15 ð1 1=rÞ 10
0:5408 1 43000
¼ 16:90 bar:
¼
0:287 373 15 ð1 1=7Þ
The maximum cycle pressure, p 3 , can be evaluated by calculating around the cycle from point 1.
Working around the cycle
k 1:4
p 2 ¼ p 1 ðrÞ ¼ 1 ð7Þ ¼ 15:25 bar:
This can be considered to be the point at which combustion (or, more accurately, energy transfer)
commenced, initiated by a spark in this case.
k 1 0:4
T 2 ¼ T 1 ðrÞ ¼ 373 7 ¼ 812:36 K:
The temperature at 3 can be evaluated from
q 23
T 3 ¼ T 2 þ
c v
The heat addition, q 23 , per unit mass of air, is
Q 0
v
q 23 ¼
ε
giving
Q 0 43000
v
T 3 ¼ T 2 þ ¼ 812:36 þ
εc v 15 0:715
¼ 4821:7K:
(Note: this temperature is much higher than that achieved in an actual engine cycle, and would
result in too high a thermal load on the structure).
It is now possible to evaluate the maximum pressure

mRT 3
p 3 ¼
V 3
but

p 1 V 1
m ¼
RT 1
and hence
p 1 V 1 RT 3 p 1 V 1 T 3 T 3
¼ p 1 r
p 3 ¼ ¼
RT 1 V 3 T 1 V 3 T 1
4821:7
¼ 90:49 bar:
¼ 1 7
373